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Renormalization, the Riemann–Hilbert Correspondence, and Motivic Galois Theory

In: Frontiers in Number Theory, Physics, and Geometry II

Author

Listed:
  • Alain Connes

    (College de France
    I.H.E.S.)

  • Matilde Marcolli

    (Max–Planck Institut für Mathematik)

Abstract

We give here a comprehensive treatment of the mathematical theory of perturbative renormalization (in the minimal subtraction scheme with dimensional regularization), in the framework of the Riemann–pHilbert correspondence and motivic Galois theory. We give a detailed overview of the work of Connes–Kreimer [31], [32]. We also cover some background material on affine group schemes, Tannakian categories, the Riemann–Hilbert problem in the regular singular and irregular case, and a brief introduction to motives and motivic Galois theory. We then give a complete account of our results on renormalization and motivic Galois theory announced in [35].

Suggested Citation

  • Alain Connes & Matilde Marcolli, 2007. "Renormalization, the Riemann–Hilbert Correspondence, and Motivic Galois Theory," Springer Books, in: Pierre Cartier & Pierre Moussa & Bernard Julia & Pierre Vanhove (ed.), Frontiers in Number Theory, Physics, and Geometry II, pages 617-713, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-30308-4_13
    DOI: 10.1007/978-3-540-30308-4_13
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